Tone control in general is the selective amplification or attenuation of particular frequency bands of an audio signal. Typically tone control systems divide the audio spectrum into a bass or low frequency band, a mid-band, and a treble or high frequency band. In tone control the bass and treble bands are independently amplified or attenuated while the amplitude response of the mid-band is maintained unaltered.
Yoshimutsu Hirata in the article "Simple Digital Filters For Sound Reproduction", Wireless World, Sept. 1982, pp. 77-79 (incorporated herein by reference) describes a sampled data tone control system realized by the cascade connection of two sampled data filters. One of these filters controls the bass response and includes the cascade combination of a recursive and a non-recursive sampled data filter having the frequency response H.sub.1 (Z) given by EQU H.sub.1 (Z)=1-AZ.sup.-1 /(1-BZ.sup.-1) (1)
where Z is the conventional Z-transform variable and A and B are variable coefficients.
The other of the two filters controls the treble response and also includes the cascade connection of a recursive and a non-recursive sampled data filter. The frequency response H.sub.2 (Z) of this filter is described by EQU H.sub.2 (Z)=(1-H)/(1-G).multidot.(1-GZ.sup.-1)/(1-HZ.sup.-1)(2)
where H and G are variable coefficients. The combined response T(Z) which is the response of the tone control apparatus is EQU T(Z)=(1-AZ.sup.-1)/(1-BZ.sup.-1).multidot.(1-GZ.sup.-1)/(1-HZ.sup.-1).multi dot.(1-H)/(1-G). (3)
Equation (3) indicates that a minimum of six scaling circuits are required to perform the tone control transfer function. If the audio signals are in digital format and defined by 16-bit samples, it will readily be appreciated by those skilled in the art of digital signal processing that the scaling circuits (e.g. multipliers) represent a substantial amount of hardware.
It is an object of the present invention to provide tone control for sampled data signals with a minimum of hardware. To this end the present inventor expanded equation (3) resulting in the expression EQU T(Z)=(1-H)[1-(A+G)Z.sup.-1 +AGZ.sup.-2 ]/(1-G)[1-(B+H)Z.sup.-1 +BHZ.sup.-2 ](4)
which is of the form EQU T(Z)=G.sub.0 .multidot.(1+b.sub.1 Z.sup.-1 +b.sub.2 Z.sup.-2)/(1-a.sub.1 Z.sup.-1 -a.sub.2 Z.sup.-2) (5)
where G.sub.0 =(1-H)/(1-G), b.sub.1 =-(A+G), b.sub.2 =AG, a.sub.1 =(B+H) and a.sub.2 =-BH. Equation (5) describes a general filter function which may be realized with a minimum parts or canonic form. While there appears to be a direct correspondence between equation (3) and equation (5) this is only a mathematical artifice. The cascade arrangement of filter functions represented by equation (3) permits simultaneous independent adjustment of both the bass and treble response. In general this is not practical with a canonic filter represented by the transfer function of equation (5). However, with appropriate selection of coefficients the canonic filter may be conditioned to provide a low-pass response or a high-pass response or a notch type response. Thus, according to the invention the canonic filter form may be arranged with selectable coefficients to boost or attenuate bass response or alternatively to boost or attenuate treble response. A third alternative, by selecting coefficients to produce a notch filter type response, is to simultaneously boost or attenuate both the bass and treble response.